Keywords: Excess zeros, Negative binomial, Marginal models, Overdispersion, Overall subject-specific effect, Random effects
The two-stage zero-inflated negative binomial regression model with random effects is used by public health researchers to assess the relationship between an exposure of interest and over-dispersed and correlated count outcomes that are heavily populated at zero, in excess of what can be assumed under the negative binomials sampling. The two sets of regression coefficients from this model provide separate inferences, first on the likelihood of being an excess zero class membership, and secondly on the intensity of the risk in the susceptible class. Thus regression coefficients from this model are not well-suited for estimating exposure effects on the overall subject-specific mean. Others have suggested post-modeling computations using these regression coefficients as inputs to estimate overall exposure effects, with the use of delta method and bootstrap techniques which could be arduous for most researchers. To allow straight forward estimation of overall exposure effects without post-modeling computations we propose the marginalized negative binomial regression model (MZINB) with random effects that jointly models the overall subject-specific mean and the excess zeros which provides estimates that allow subject-specific marginal mean inference, after adjusting for extra zeros. The MZINB model with random effects is applied to the CombiRx clinical trial data to assess whether the combine use of glatiramer acetate and interferon beta-la is better than either therapy alone in reducing the formulation of new lesions in the overall sampled population of multiple sclerosis patients randomized to the treatment groups.